From what I understand conquering a country usually means by military force and to annex a country means that the annexed country wanted to join to the annexer. (it's a word now) did all the countries that the USSR annex (Poland, Baltic states, Albania, ect.) Do so willingly? Also I keep reading that the USSR occupied their annexed country's with military forces, which kind of sounds like what happened when a country is conquered. Any clarification is much appreciated
There are two separate issues here. To take them in turn:
Annexation doesn't imply consent, it just denotes addition of another (usually smaller) territory to your own, which may or may not be welcomed by the local population: if it's been approved by a local plebiscite or by local representatives we might speak more commonly of union or reunification. So we don't generally speak of Denmark annexing northern Schleswig in 1920, because it was subject to an internationally-supervised plebiscite.
But as others have pointed out, the USSR didn't annex Poland or Albania after the war, they became part of its sphere of influence (and Albania's affiliation was never very certain, ending in 1960). The USSR did annex the Baltic states, parts of eastern Poland, Ruthenia (the Ukranian/Rusyn-majority easternmost part of interwar Czecholsovakia), and the formerly Romanian-held territories of northern Bukovina (Ukrainian-majority) and Bessarabia (Moldovan, Ukrainian and other), along with border areas of Finland.
The rest of the eastern European countries were governed by local communist parties more or less subject to Moscow (Yugoslavia broke away as early as 1948 while Romania pursued its own course in the 1960s as did Poland and Hungary to a lesser extent, the last mostly in the economic sphere). But they remained technically independent states subject in varying degrees to the possibility of political troublemaking, economic arm-twisting or military intervention (none of them techniques entirely alien to other world powers) if they stepped too far out of line.
Can you specify the period? If you are talking about post WW2, the USSR didn’t annexe much more land than originally planned between the Allies in Posdam (July 1945). A part of Europe was under military occupation by the Red Army. As planed by inter-Allies agreements, election took place in occupied territories. But once the new governments elected, the USSR slowly transformed the new democracy into popular democracy by exercising pressures with the Red Army, by favorising the communist Party, banning opposition parties, etc etc. At the end, Eastern European countries choose to join the Eastern Bloc, they were not annexed (even if on the field the Red Army had the real power), constitutionally, those countries stayed independent countries. But we all know that in reality, they were under the orders of Moscow.
So, this is actually a good question to talk about what hegemony is. You are correct in noting that conquest has rather military connotations, while annexation is a more diplomatic way of acquiring territory. However, both of these modes of territorial expansion involve the borders of the conquering or annexing nation to subsequently include those of the conquered or annexed nation. But this is not what happened in the immediate postwar period pertaining to the Eastern Bloc. These states (ie. Poland, Hungary, Romania, East Germany, etc) remained, in the broadest possible definition, independent and sovereign from the Soviet Union with their own governments and institutions. I specify that such a definition is broad because of the nature of hegemony. Hegemony is the control of a state by another state on a political, economic, or even cultural level. Therefore while a state like Poland could have its own government, institutions, and culture, they were greatly influenced by the hegemonic state in whose sphere of influence Poland was situated, that being the Soviet Union. This is what constitutes a satellite state.
Whether or not such hegemony was welcomed by the states of the Eastern Bloc is a little foggy. At the height of its power, Nazi Germany controlled, occupied, or was allied with nearly the entirety of the European continent. Some of their most valuable assets in Europe were puppet states that were established in Eastern Europe, headed by strongmen with fascist sympathies that would comply with German demands, the most well-known of which was Philippe Pétain of Vichy France. Naturally, there was opposition against the fascist takeovers of entire nations. More times than not, the groups at the forefront of the opposition were communist insurgent groups. The Yugoslav Partisans, the First Czechoslovak Partisan Brigade, the Polish Armia Ludowa and others were all either led by or were made up of a large number of communists. After the Third Reich’s downfall in 1945, communism in Eastern and Central European became a major power player because of their role in the defeat of the fascists. Communists came to power in one way or another throughout the Eastern European countries. Some electoral victories were secured by communist parties, but such victories were achieved mainly because certain political parties were banned because of suspected collaboration with fascists, like in Poland and Albania. In Yugoslavia, the opposition boycotted the 1945 elections, leading to a communist and socialist majority in the legislature. So these countries' alliance with the Soviets was certainly welcomed by some, opposed by others.
Very typically, in terms of the Cold War, hegemony was practiced by way of political, economic, and cultural influence in exchange for military protection. A smaller country sacrifices some of its sovereignty to a hegemonic power in exchange for that power's military protection and political support. The United States practiced the same form of hegemony, namely throughout the rest of the American continent as well as Western Europe. This was why the United States had troops stationed throughout their own sphere of influence. This is why the United States still maintains military bases in friendly countries throughout the world today, such as Germany, Italy, Spain, Brazil, Honduras, among many others.
That's as clear-cut and simple of an explanation I could muster. The countries of the Eastern Bloc were, technically, independent, but were under the hegemonic control of the Soviet Union. Therefore, the Soviets could not exert direct political control over these countries, but rather held great amounts of influence over these countries' institutions. Check these books out for further reading: